Rupert Everett, an openly gay actor, with Christopher Walken in a still from The Comfort of Strangers. Photograph: Skouras Pictures/Rex Features

When Antony Sher started acting with the pioneering Gay Sweatshop theatre company in the 70s, he managed to stay in the closet. "I look back and blush," he said. "We all agreed to do it on the basis that it was stated that not all the performers were gay so you didn't know who was and who wasn't.

"Then, in the mid-80s, when I did the British premiere of Harvey Fierstein's Torch Song Trilogy, I still wasn't out. I was doing press interviews about this great gay play that I felt so strongly about for a specific reason and I wasn't saying it – it was an astonishing waste of energy. But that's the kind of tangle you get into if you're not out."

Sher finally came out in 1990, inspired by the example of Ian McKellen and Simon Callow. Yet, more than two decades on, despite strides in gay equality and the entertainment industry's liberal reputation, many gay actors still fear that being open about their sexuality will damage their careers.

In 2006, the actor Chris New, who starred in the film Weekend last year, was advised by his agent not to talk about being gay, despite starring at the time in Bent, Martin Sherman's play about the persecution of gay people in Nazi Germany.

Now Equity has enlisted several well-known actors to lend their names to a campaign supporting gay actors who choose to come out. "It's about giving members the confidence to come out and if they do, that we'll be there to offer them support," said Max Beckmann, Equity's equalities officer.

"If actors experience homophobic bullying we would be able to raise that with the employer or if there was a case of member discrimination we would offer them legal assistance."

New said he knew of a fellow gay actor "who's in LA and making films, and he's taking very visible steps to go back in the closet. A lot of people have warned me about being out in America. They say: 'Maybe you should back off from playing too many gay roles' and 'Don't do too much gay press'."

Sher said that Hollywood was reluctant to give roles to out gay actors, because it was trying to get the biggest possible mainstream audience. "Test audiences are midwestern, very conservative people, so it's possible that those kinds of people would be uncomfortable watching a gay man play a sex scene with a woman or whatever. But the world is changing, so that audience is going to change as well."

He agreed with the time-honoured belief of gay campaigners that coming out is the only way to change things. "If everybody came out of the closet, [being gay] would cease to be an issue because there would be so many of us. Ian McKellen is the first out actor to be nominated for an Oscar – when people start doing things like that then things change.

"Role models are terribly important. I speak as one who grew up in apartheid South Africa where it was not just illegal but it was like the most disgusting, criminal thing you could possibly be doing. It would have been transforming as a teenager to have seen people like Ian McKellen and my own partner, Greg, being talked about on their merits and not on their sexuality."

Sophie Ward, one of the few out gay female actors, agreed that sexuality would only stop being an issue when out gay actors became so commonplace they no longer attracted any special attention. "Actors don't want it to be the first thing they have to discuss every time they talk about their career," she said. "But it will always be an issue until everybody feels comfortable coming out – it's a circular argument."

Sher said: "I'm sorry if that's the case for him, but he seems to have had quite a big career out of playing outrageous and camp characters. He hasn't done badly, has he?"

Though New was recently turned down for the role of Jesus on a US TV show, and suspects it was because he is gay, he said that actors should not blame homophobia for not getting cast in the roles they want.

"There could be a million reasons why you might not get a job and gay people have to be careful about blaming [homophobia], because they're reinforcing their own closet door.

"First, there's nothing you can do about it except wait for people's opinions to change, which they do. There are a lot of actors I know who are black who constantly say: 'I need to go to America because I don't get any jobs over here.' Most of these people, usually, are having quite nice careers. It can become an obsession."

New said that rather than become obsessed with not landing heterosexual romantic leads, he was relaxed about playing gay roles. "I have played quite a few gay roles but they've been really good. Weekend is a really good gay role. Bent is incredible. Obviously I do get sent scripts which have pretty rubbish gay roles. All you can do is say yes to the things you want to do and no to the things you don't."

He added that actors pay a heavy personal price for staying in the closet. "Let's say you were dating an actor who was in the closet. It would be a very bad thing to be able to say: 'Oh, I'm dating this guy but I'm not allowed to say who it is.' That'd be a bit of an ugly world to live in. There are quite a few actors who are in the closet who I just challenge. They usually um and ah and say: 'You don't understand.' First, why would anybody be that interested – it's kind of vanity to think that anybody would. And second, just get on with it and stop lying about yourself."

Malcolm Sinclair, Equity's president, said that coming out would have a positive impact on actors' work: "Acting at its finest is about telling the truth, so being honest about yourself is always going to benefit your craft."

Sher concurs. "When you see any great performer, you sort of see into that person's soul," he said. "Your sexuality is profoundly a part of who you are. I think it's very difficult to really reveal yourself in that exquisite way if you're trying to hide part of yourself."